Markov chains in the twohyphen;dimensional Ising model: Multibody interactions and Polandrsquo;s exact solution

摘要

For certain interaction parameters, onehyphen;dimensional paths between points on the twohyphen;dimensional planehyphen;square Ising lattice gas behave like Markov chains. Poland has reduced the determination of these interactions to a single nonlinear equation with two free parameters. However, this equation neglects the effects of threehyphen;body and fourhyphen;body interactions. Strengths of these interactions are computed, and conditions are given under which the lattice has only twohyphen;body interactions. Determination of such models is again reduced to a single (polynomial) equation, but with only one free parameter.